Problem: Express your answer as a mixed number simplified to lowest terms. $18\dfrac{1}{15}-10\dfrac{2}{3} = {?}$
Answer: Find a common denominator for the fractions: $= {18\dfrac{1}{15}}-{10\dfrac{10}{15}}$ Convert ${18\dfrac{1}{15}}$ to ${17 + \dfrac{15}{15} + \dfrac{1}{15}}$ So the problem becomes: ${17\dfrac{16}{15}}-{10\dfrac{10}{15}}$ Separate the whole numbers from the fractional parts: $= {17} + {\dfrac{16}{15}} - {10} - {\dfrac{10}{15}}$ Bring the whole numbers together and the fractions together: $= {17} - {10} + {\dfrac{16}{15}} - {\dfrac{10}{15}}$ Subtract the whole numbers: $=7 + {\dfrac{16}{15}} - {\dfrac{10}{15}}$ Subtract the fractions: $= 7+\dfrac{6}{15}$ Combine the whole and fractional parts into a mixed number: $= 7\dfrac{6}{15}$ Simplify to lowest terms: $= 7\dfrac{2}{5}$